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Updated: Jul 16, 2026
06:07
Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
Stability analysis of dynamic ratcheting in elastoplastic systems.
Noël Challamel1, Christophe Lanos, Abdelaziz Hammouda
1Laboratoire de Génie Civil et Génie Mécanique, INSA de Rennes, 20 Avenue des Buttes de Coësmes, 35043 Rennes Cedex, France. noel.challamel@insa-rennes.fr
Summary
This study analyzes the stability and dynamics of an asymmetrical oscillator. Oscillator asymmetry, whether in material or boundary conditions, significantly impacts its divergence rate and vibration behavior.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Materials Science
Background:
- Harmonically excited elastic perfectly plastic oscillators exhibit complex hysteretical behavior.
- Asymmetrical systems present unique challenges in stability and dynamic analysis.
- Understanding the transition between elastoplastic shakedown and dynamic ratcheting is crucial for structural integrity.
Purpose of the Study:
- To investigate the stability and dynamics of a harmonically excited elastic perfectly plastic asymmetrical oscillator.
- To explore the influence of asymmetry in boundary conditions and material properties on system behavior.
- To provide a closed-form solution for the boundary between elastoplastic shakedown and dynamic ratcheting.
Main Methods:
- Formulating the hysteretical system as a nonsmooth, forced autonomous system.
- Reducing phase space dimension using adapted variables.
- Employing numerical time-locating techniques for forced vibration analysis.
- Utilizing a perturbation approach for analytical investigation of limit cycle stability.
Main Results:
- Asymmetry in boundary conditions and material properties leads to an equivalent system.
- Stability of limit cycles is analytically determined.
- A closed-form expression for the elastoplastic shakedown and dynamic ratcheting boundary is derived.
- The oscillator's internal asymmetry is strongly correlated with its divergence rate.
Conclusions:
- The study provides a comprehensive analysis of asymmetrical oscillator dynamics.
- Asymmetry is a key factor influencing the stability and vibration characteristics of such systems.
- The findings offer valuable insights for designing and analyzing structures with potential asymmetries.
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